Determination of the stress distributions induced by inclusions has aroused considerable interest for more than half a century. Several analytical solutions were presented in the literature. Some of them consider special loading conditions such as uniform loading or a concentrated couple (Chen, 1967b; Yang and Chou, 1976; Hwu and Ting, 1989), some others consider special matrices such as isotropic matrix (Eshelby, 1957; Jaswon and Bhargave, 1961; Sendeckyi, 1970; Stagni, 1982), or special inclusions such as rigid inclusions or holes (Santare and Keer, 1986; Hwu and Yen, 1991; Hwu and Wang, 1992), or special shapes such as lines or circles (Wang et al., 1985; Honein and Herrmann, 1990), or the uncoupling of in-plane and anti-plane deFormations. A unified general analytical solution for the elliptical anisotropic elastic inclusions imbedded in an infinite anisotropic matrix subjected to an arbitrary loading was introduced by Hwu and Yen (1993). The presentation of this chapter will then follow mainly that of Hwu and Yen (1993) and their follow-up discussions about the interactions between inclusions and dislocations (Yen and Hwu, 1994; Yen et al., 1995) and the interactions between inclusions and cracks (Hwu et al., 1995b).